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Solve the equations for [tex]\( x \)[/tex] and match the solutions.

[tex]\[
\begin{array}{ll}
x=-\frac{3}{a} \quad x=\frac{6}{a} \quad x=-\frac{a}{6} \quad x=-\frac{6}{a} \quad x=\frac{3}{a} \\
x=\frac{a}{6} & x
\end{array}
\][/tex]

1. [tex]\(-ax - 20 = -14\)[/tex]
[tex]\(\square\)[/tex]

2. [tex]\(4 = \frac{6}{a} x + 5\)[/tex]
[tex]\(\square\)[/tex]

3. [tex]\(7 + 2ax = 13\)[/tex]
[tex]\(\square\)[/tex]


Sagot :

To solve each equation for [tex]\( x \)[/tex] and match the solutions:

1. Equation: [tex]\(-a x - 20 = -14\)[/tex]

- First, isolate [tex]\( -a x \)[/tex]:
[tex]\[ -a x - 20 + 20 = -14 + 20 \implies -a x = 6 \][/tex]
- Then, solve for [tex]\( x \)[/tex]:
[tex]\[ x = -\frac{6}{a} \][/tex]

Therefore, [tex]\(-a x - 20 = -14 \implies x = -\frac{6}{a}\)[/tex].

2. Equation: [tex]\(4 = \frac{6}{a} x + 5\)[/tex]

- First, isolate [tex]\(\frac{6}{a} x\)[/tex]:
[tex]\[ 4 - 5 = \frac{6}{a} x + 5 - 5 \implies -1 = \frac{6}{a} x \][/tex]
- Then, solve for [tex]\( x \)[/tex]:
[tex]\[ x = -\frac{a}{6} \][/tex]

Therefore, [tex]\(4 = \frac{6}{a} x + 5 \implies x = -\frac{a}{6}\)[/tex].

3. Equation: [tex]\(7 + 2 a x = 13\)[/tex]

- First, isolate [tex]\(2 a x\)[/tex]:
[tex]\[ 7 + 2 a x - 7 = 13 - 7 \implies 2 a x = 6 \][/tex]
- Then, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{a} \][/tex]

Therefore, [tex]\(7 + 2 a x = 13 \implies x = \frac{3}{a}\)[/tex].

Matching the solutions to each equation:

[tex]\[ \begin{array}{ll} -a x - 20 = -14 & \quad x = -\frac{6}{a} \\ 4 = \frac{6}{a} x + 5 & \quad x = -\frac{a}{6} \\ 7 + 2 a x = 13 & \quad x = \frac{3}{a} \end{array} \][/tex]